We study the scattering of the ϕ 8 kinks off each other, namely, we consider those ϕ 8 kinks that have power-law asymptotics. The slow power-law fall-off leads to a long-range interaction between the kink and the antikink. We investigate how the scattering scenarios depend on the initial velocities of the colliding kinks. In particular, we observe the 'escape windows' -the escape of the kinks after two or more collisions, explained by the resonant energy exchange between the translational and vibrational modes. In order to elucidate this phenomenon, we also analyze the excitation spectra of a solitary kink and of a composite kink+antikink configuration.

We study the scattering of kink and antikink of the double sine-Gordon model. There is a critical value of the initial velocity v cr of the colliding kinks, which separates different regimes of the collision. At v in > v cr we observe kinks reflection, while at v in < v cr their interaction is complicated with capture and escape windows. We obtain the dependence of v cr on the parameter of the model. This dependence possesses a series of local maxima, which has not been reported by other authors. At some initial velocities below the critical value we observe a new phenomenon -the escape of two oscillons in the final state. Besides that, at v in < v cr we found the initial kinks' velocities at which the oscillons do not escape, and the final configuration looks like a bound state of two oscillons.

We consider the scattering of kinks of the sinhdeformed ϕ 4 model, which is obtained from the well-known ϕ 4 model by means of the deformation procedure. Depending on the initial velocity v in of the colliding kinks, different collision scenarios are realized. There is a critical value v cr of the initial velocity, which separates the regime of reflection (at v in > v cr ) and that of a complicated interaction (at v in < v cr ) with kinks' capture and escape windows. Besides that, at v in below v cr we observe the formation of a bound state of two oscillons, as well as their escape at some values of v in .

We study a model described by a single real scalar field in the two-dimensional space-time. The model is specified by a potential which is non-polynomial and supports analytical kink-like solutions that are similar to the standard kink-like solutions that appear in the ϕ 4 model when it develops spontaneous symmetry breaking. We investigate the kinkantikink scattering problem in the non-polynomial model numerically and highlight some specific features, which are not present in the standard case.

We study the scattering of the ϕ 8 kinks with power-law asymptotics. We found two critical values of the initial velocity, v arXiv:1712.02846v1 [hep-th]

We study the properties of a relativistic model with logarithmic nonlinearity.We show that such model allows two types of solutions: topologically trivial (gaussons) and topologically non-trivial (kinks), depending on a sign of the nonlinear coupling. We focus primarily on the kinks' case and study their scattering properties. For the kink-antikink scattering, we have found a critical value of the initial velocity, which separates two different scenarios of scattering. For the initial velocities below this critical value, the kinks form a bound state, which then decays slowly. If the initial velocities are above the critical value, the kinks collide, bounce and eventually escape to infinities. During this process, the higher initial velocity is, the greater is the elasticity of the collision. We also study excitation spectrum of the kink solution.

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We study the kink-antikink scattering within the double sine-Gordon model. In the numerical simulations we found a critical value vcr of the initial velocity vin, which separates two different scenarios: at vin < vcr the kinks capture each other and form a bound state, while at vin > vcr the kinks pass through each other and escape to infinities. We obtain non-monotonous dependence of vcr on the model parameter R. Besides that, at some initial velocities below vcr we observe formation and interaction of the so-called oscillons (new phenomenon), as well as escape windows (well-known phenomenon).